Many DAWs have the option to "quantize" a set of notes. What does it do?
Quantization aligns (or "snaps") the MIDI data (usually musical notes) to the tempo (or subdivisions, thereof) of the composition. You can think of it as an automatic "clean-up" for MIDI data that was close to exact, but not quite exact.
It will often have configurable options, such as quantize to 1/4 notes, 1/8 notes, 1/16 notes, etc... (subdivisions of the project tempo).
I'll quote Wikipedia's article, because they put it well:
In digital music processing technology, quantization is the process of aligning a set of musical notes to a precise setting. This results in notes being set on beats and on exact fractions of beats. ...the dimensions of this timing grid are set beforehand. When one instructs the music application to quantize a certain group of MIDI notes in a song, the program moves each note to the closest point on the timing grid.
I use an analogy to illustrate what quantization is.
Imagine that a beat is like the rung of a ladder. An entire ladder with sixteen rungs is like a measure with sixteen notes.
While climbing the ladder, your foot can aim for any rung or land anywhere near a rung, but it will always end up exactly on a rung.
Quantization is the process that pushes your foot to one rung or the other.
Does this make sense?